If I'm running on a road, which is not often, it's a road that has little to no traffic. This usually gives me a chance, when I notice a car coming from either behind or ahead, to switch to the opposite side of the road from the car. That's usually safer than staying on one side.
On a narrow twisting road, like in canyons, I stay on the side that has more visibility for drivers to see me. Running against traffic would be asking to be hit. Think about if you are on the inside of the corner with the mountainside or a hedge to your left and no shoulder. The on-coming cars and you would have a very limited sight line, and you'd see each other with almost no time to react, especially if they are "performance" driving, and you'd have no place to jump off the road.
In many situations, it is safer to run against traffic, but running with traffic isn't any more dangerous than riding a bike. Cyclists might go running speed or slower on some mountain roads. When running with traffic, be aware of situations like running towards a setting sun, where a driver behind you has to squint and the sun washes out their vision. Or if it's dark or getting dark. Sometimes it's better to preemptively get off the road and wait for a car to pass. If run really odd hours like I have at times, be aware of when drunk drivers are more likely to be around at night/weekends, and get off the road when a car comes near.